The scheme of antenna wrapping around a quartz tube has been employed widely for inductively coupling and helicon discharges[1]}, [2]}, [3]}. This electrodeless feature can lead to long life and high efficiency, due to the absence of electrode erosion and plasma sheath, respectively. To further increase the plasma density and temperature, together with particle energy, multiple antennas were conceived and implemented, such as VASIMR (VAriable Specific Impulse Magnetoplasma Rocket)[4]}, HEAT (Helicon Electrodeless Acceleration Thruster)[5]} and other experiments[6]}, [7]}, [8]}, [9]}. However, the mutual coupling between these coaxial antennas, which are separated axially with a certain distance, through the same plasma cylinder was rarely studied. This coupling can result in significant magnitude of voltage and current on neighbouring antennas and, according to the Faraday's law and the conservation of magnetic flux, they are generally in the opposite direction to those originally provided by their power supplies. With regard to plasma generation, this surely weakens the ionisation rate and heating efficiency. Thereby, it is of great importance to investigate the coupling physics between these antennas, and guide experiments to either reduce the coupling effect or turn the detrimental coupling into beneficial usage. Here, we explore the coupling physics on a recently built device which employs three antennas around a helicon plasma cylinder, and through analyses from the perspectives of transformer and magnetic permeability.
